The primary objectives are: (i) To determine if the addition of carotid endarterectomy (CE) to optimum medical care for patients with TIA or partial stroke and moderate (30-69%) carotid stenosis, reduces the risk of subsequent stroke and stroke-related death; and (ii) To enquire if symptomatic patients with severe stenosis, proven by the first phase of this study to benefit from carotid endarterectomy, after prolonged follow- up, continue to demonstrate the superiority of surgery over medical care alone. The Trial will adhere to the essentials of the protocol established for the patients with severe (70-99%) and for moderate (30-69%) stenosis as was followed between January 3,1988 and February 21, 1991 but after this latter date, recruitment has been confined to patients in the moderate group. The follow-up will involve the 659 patients already in the severe group, the 1066 patients in the moderate group who will be entered by the end of year 5, plus an additional 1018 patients entered between 1992 and 1996. 2084 patients are required if we are to be able to distinguish benefit for those with 50-69% stenosis as compared to benefit for those with only 30-49%. Present recruitment indicates clearly that the 82 centers now active can complete the entry and average follow-up within a 2nd five-year Grant term. A relentless drive to increase the number of randomized patients will continue so as to reduce even further, if possible, the time needed to complete the task. Adequate carotid angiography is mandated prior to randomization. Baseline ultrasound studies are required and will be repeated in medical and surgical patients at 30 days after entry, after an outcome, event, at annual intervals and at the conclusion of the Trial. Progression beyond 70% in patients continuing to have symptoms will lead, if confirmed by arteriography, to a recommendation for Surgery. "Alerting rules" will ensure that the study will be stopped if there is evidence of harm to patients in the moderate group because of unexpectedly higher morbidity from endarterectomy compared to medical therapy, or because significant benefit is detected in the surgical limb of the study population. Excluded will be patients: Without accessible arteriosclerotic disease appropriate to their symptoms; without symptoms; without informed consent; with a progressing or disabling deficit; with recent Myocardial Infarction; or with organ failure. Patients will be seen at 3 monthly intervals in the first year, 3 times yearly thereafter, will be documented for all recognized risk factors, and will ~e monitored for control of hypertension and for use of appropriate anti-thrombotic agents.